diff options
| -rw-r--r-- | transverse/decompose.m | 55 |
1 files changed, 33 insertions, 22 deletions
diff --git a/transverse/decompose.m b/transverse/decompose.m index e9b583a..7b8fd53 100644 --- a/transverse/decompose.m +++ b/transverse/decompose.m @@ -1,9 +1,9 @@ %----------------------------------------------------------------------------------------------
% PROGRAM: decompose
-% AUTHOR: Andri M. Gretarsson
+% AUTHOR: Andri M. Gretarsson, edited by Melissa Guidry
% DATE: 7/10/04
%
-% SYNTAX: [coeffs,tmat]=decompose(z1,domain,type,terms,[q <,lambda,accuracy>]);
+% SYNTAX: [coeffs,tmat]=decompose(z1,domain,type,terms,[q <,lambda,accuracy>],coordtype);
% <...> indicates optional arguments
%
% Calculates the coefficients of the decomposition of the function z1 into
@@ -67,6 +67,11 @@ % of 1.54 would be rounded to 1.5 while a coefficient of 1.56 would be
% rounded to 1.8. Accuracy of 0 applies no rounding. Specifying
% accuracy other than "0" does not speed up the calculation.
+% coordtype = (string) label for the type of coordinates supplied in r and theta. If
+% this argument is equal to 'pol', r and theta are assumed
+% to be polar coordinates (r,theta) as described above. If on the other
+% hand coordtype='cart' then r is assumed to be the cartesian x coordinate
+% and theta the cartesian y coordinate.
%
% OUTPUT ARGUMENTS:
% -----------------
@@ -88,7 +93,7 @@ % [x,y]=meshgrid([-pi/2:0.1:pi/2],[-pi/2:0.1:pi/2]); z1=cos(sqrt(x.^2+y.^2));
% clear domain; domain(:,:,1)=x; domain(:,:,2)=y;
% w=pi/4; R=1e3; lambda=1e-6; q=(1./R - i* lambda./pi./w.^2).^(-1);
-% [coeffs,tmat]=decompose(z1,domain,'hg',140,[q,lambda,1e-6])
+% [coeffs,tmat]=decompose(z1,domain,'hg',140,[q,lambda,1e-6],'cart')
% z1recomposed=recompose(domain,'hg',coeffs,[q,lambda,1e-6]);
% subplot(3,1,1); h=pcolor(x,y,abs(z1).^2); set(h,'EdgeColor','none'); axis square; colorbar
% subplot(3,1,2); h=pcolor(x,y,abs(z1recomposed).^2); set(h,'EdgeColor','none'); axis square; colorbar
@@ -96,9 +101,15 @@ %
% Last updated: July 18, 2004 by AMG
%----------------------------------------------------------------------------------------------
-% SYNTAX: [coeffs,tmat]=decompose(z1,domain,type,terms,[q <,lambda,accuracy>]);
+% SYNTAX: [coeffs,tmat]=decompose(z1,domain,type,terms,[q <,lambda,accuracy>],coordtype);
%----------------------------------------------------------------------------------------------
-function [coeffs,tmat]=decompose(z1,domain,type,terms,params)
+function [coeffs,tmat]=decompose(z1,domain,type,terms,params,coordtype)
+
+if strcmpi(coordtype,'cart')
+ metric = 1;
+elseif strcmpi(coordtype, 'pol')
+ metric = domain(:,:,1);
+end
% HERMITE GAUSSIAN EXPANSION --------------------------------------------------------------------------
if strcmpi(type,'hg')
@@ -109,10 +120,10 @@ if strcmpi(type,'hg') if size(terms,1)==1 && size(terms,2)==1 % Make terms request matrix
n=ceil(sqrt(terms));
tmat=ones(n,n);
- if n^2>terms
- tmat(end,end-ceil((n^2-terms)/2)+1:end)=0;
- tmat(end-floor((n^2-terms)/2):end-1,end)=0;
- end
+ %if n^2>terms
+ % tmat(end,end-ceil((n^2-terms)/2)+1:end)=0;
+ % tmat(end-floor((n^2-terms)/2):end-1,end)=0;
+ %end
else
tmat=terms;
end
@@ -123,7 +134,7 @@ if strcmpi(type,'hg') m=t-1;
if tmat(s,t)==1
z2=HermiteGaussianE([l,m,q,lambda],domain(:,:,1),domain(:,:,2));
- coeffs(s,t)=overlap(z1,conj(z2),domain,1,accuracy);
+ coeffs(s,t)=overlap(z1,conj(z2),domain,metric,accuracy);
else
coeffs(s,t)=0;
end
@@ -138,14 +149,14 @@ elseif strcmpi(type,'lg') if size(terms,1)==1 && size(terms,2)==1 % Make terms request matrix
n=ceil( (1+sqrt(1+8*terms))/4 );
tmat=ones(n,n,2); tmat(:,1,2)=0;
- ndiff=2*n^2-n-terms;
- if ndiff>0
- rdiff=ceil(ndiff/2); ldiff=floor(ndiff/2);
- tmat(end,end-ceil(rdiff/2)+1:end,1)=0;
- tmat(end-floor(rdiff/2):end-1,end,1)=0;
- tmat(end,end-ceil(ldiff/2)+1:end,2)=0;
- tmat(end-floor(ldiff/2):end-1,end,2)=0;
- end
+ %ndiff=2*n^2-n-terms;
+ %if ndiff>0
+ % rdiff=ceil(ndiff/2); ldiff=floor(ndiff/2);
+ % tmat(end,end-ceil(rdiff/2)+1:end,1)=0;
+ % tmat(end-floor(rdiff/2):end-1,end,1)=0;
+ % tmat(end,end-ceil(ldiff/2)+1:end,2)=0;
+ % tmat(end-floor(ldiff/2):end-1,end,2)=0;
+ %end
%disp(' '); dispmat(tmat(:,:,1)); disp(' '); dispmat(tmat(:,:,2)); disp(' '); disp(num2str(sum(sum(sum(tmat)))));
else
tmat=terms;
@@ -158,14 +169,14 @@ elseif strcmpi(type,'lg') for t=1:size(tmat,2)
m=t-1;
if tmat(s,t,1)==1 % coeff requested
- z2=LaguerreGaussianE([p,m,q,lambda],domain(:,:,1),domain(:,:,2),'pol');
- coeffs(s,t,1)=overlap(z1,conj(z2),domain,domain(:,:,1),accuracy);
+ z2=LaguerreGaussianE([p,m,q,lambda],domain(:,:,1),domain(:,:,2),coordtype);
+ coeffs(s,t,1)=overlap(z1,conj(z2),domain,metric,accuracy);
else
coeffs(s,t,1)=0;
end
if tmat(s,t,2)==1 % coeff requested
- z2=LaguerreGaussianE([p,-m,q,lambda],domain(:,:,1),domain(:,:,2),'pol');
- coeffs(s,t,2)=overlap(z1,conj(z2),domain,domain(:,:,1),accuracy);
+ z2=LaguerreGaussianE([p,-m,q,lambda],domain(:,:,1),domain(:,:,2),coordtype);
+ coeffs(s,t,2)=overlap(z1,conj(z2),domain,metric,accuracy);
else
coeffs(s,t,2)=0;
end
|